Finite element analysis (FEA) is a computer implemented method widely used in industry to model and solve engineering problems relating to complex systems such as three-dimensional non-linear structural design and analysis. FEA derives its name from the manner in which the geometry of the object under consideration is specified. With the advent of the modern digital computer, FEA has been implemented as FEA software. Basically, the FEA software is provided with a model of the geometric description and the associated material properties at each point within the model. In this model, the geometry of the system under analysis is represented by solids, shells and beams of various sizes, which are called elements. The vertices of the elements are referred to as nodes. The model is comprised of a finite number of elements, which are assigned a material name to associate with material properties. The model thus represents the physical space occupied by the object under analysis along with its immediate surroundings. The FEA software then refers to a table in which the properties (e.g., stress-strain constitutive equation, Young's modulus, Poisson's ratio, thermal conductivity) of each material type are tabulated. Additionally, the conditions at the boundary of the object (i.e., loadings, physical constraints, heat flux, etc.) are specified. In this fashion a model of the object and its environment is created.
FEA is becoming increasingly popular with automobile manufacturers for designing and optimizing many aspects of manufacturing of a vehicle such as aerodynamic performance, structural integrity, part manufacturing, etc. Similarly, aircraft manufacturers rely upon FEA to predict airplane performance long before the first prototype is ever developed. One of the popular FEA tasks is to simulate metal forming (e.g., sheet metal stamping or metal part forming)
Metal forming is referred to as a process of manufacturing of thin sheet metal parts or workpieces (e.g., fenders, channels, hub caps, stiffeners, etc.). It involves stretching, drawing and bending a sheet of metal into a desired shape using a hydraulic press 100 that includes at least one upper tool or punch 112 and one lower tool or die 114 shown in FIG. 1. Stamped metal parts 113 are created when the punch 112 is pressed onto the die 114 in a downward direction shown by arrow 110. Metal forming may also be referred to as a process of manufacturing metal fasteners such as bolts, screws or rivets. Many of the metal forming process require heat to soften the metal (e.g., sheet, bar, tube, wire, etc.) before pressure is applied to alter the shape of the metal to a desired shape.
During hot metal forming process, the heat is transferred from the heated metal piece 113 to the die when the punch 112 is pressed to the die 114 each time. In producing certain metal parts, the die 114 needs to be cooled down to a particular temperature range after one or more presses. Instead of cooling naturally, using a cooling system can increase the cooling efficiency thus increasing productivity of the metal-forming press. Generally, faster cooling can be achieved with cooling fluids flowing through one or more cooling fluid passages 115, which generally are embedded inside the die 114. Certain arrangements or placements of the cooling fluid passages 115 would increase cooling efficiency thereby increasing productivity further. However, the die 114 is a very expensive to manufacture. Physical trial-and-error approaches to experimental determine the best arrangement of cooling passages is too costly.
Therefore, it would be desirable to have a computer implemented method of simulating thermal fluid-structure interaction of bulk flow fluid in finite element analysis used for designing a structure, for example, thermal interaction between cooling fluids and a die of a metal forming press.